There is more than one way to compute the generalized barycentric weights \(\beta _{i,j}\) . The fastest way that we know is the algorithm of [1]}, which internally uses a confluent Newton basis. Unfortunately, because it does so, it inherits the poor numerical stability of that approach. The codes referred to above use a direct local Laurent series expansion method instead, as outlined in [2]} for instance; this method is slower but much more stable. As discussed in [3]}, however, it becomes less stable for higher confluency and cannot be perfectly backward stable even for \(s_i \ge 3\) .
We will see an example in section REF .
